The linearized model of a particular network link working under TCP$/$IP and controlled using a random early detection $($RED$)$ algorithm can be described by Figure $13$ where G$($s$)=$M$($s$)$P$($s$)$;H$($s$)=1,$ and $($Hollot$,2001)$ M$($s$)=(0\mathrm{.}005$L$)/($s$+0\mathrm{.}005)$;P$($s$)=(140625$e$^(-0\mathrm{.}1$s$))/(($s$+2\mathrm{.}67)($s$+10))$ Figure $13$ Simplified block diagram In the TCP$/$IP network link, let L$=0\mathrm{.}8,$ but assume that the amount of delay is an unknown variable. e$.$ Plot the Nyquist diagram of the system for zero delay, and obtain the phase margin. f$.$ Find the maximum delay allowed for closed$-$loop stability.